Численные методы интегрирования — различия между версиями

  1 //Монте-Карло
  2 window.addEventListener("load", program_code, false);
  3 function program_code() {
  4 
  5 	var ctx = canvas_example.getContext("2d");
  6 	var w = canvas_example.width;
  7 	var h = canvas_example.height;
  8 
  9 	ctx.translate(w/2, h/2);
 10 
 11 	var x = [];
 12 	var y = [];
 13 	var min = 1000;
 14 	var max = -1000;
 15 	var n = 0;
 16 	var points;
 17 	var cur_points;
 18 	var ok = 0;
 19 	var a;
 20 	var b ;
 21 	var scalex, scaley;
 22 	var dx;
 23 	var dy;
 24 	var func;
 25 	var time = 5000;
 26 	var dt;
 27 	var flag = false;
 28 
 29 
 30 	var result;
 31 
 32 
 33 
 34 	//функция
 35 	function f(x){
 36 		return (eval(func));
 37 	}
 38 
 39 	function search(){
 40 
 41 		func = document.getElementById("fun").value;
 42 
 43 		for (var i = a; i < b; i+=0.001){
 44 
 45 			//максимум
 46 			if (f(i) > max){
 47 				max = f(i);
 48 			}
 49 
 50 			//минимум
 51 			if (f(i) < min){
 52 				min = f(i);
 53 			}
 54 		}
 55 
 56 		//масштаб
 57     scaley = 100/(Math.abs(max) + Math.abs(min));
 58 
 59 		if (Math.abs(b) >= Math.abs(a)){
 60 			scalex = 250/b * 0.9;
 61 		}
 62 
 63 		if (Math.abs(b) < Math.abs(a)){
 64 			scalex = 250/Math.abs(a) * 0.9;
 65 		}
 66 
 67     //сдвиг
 68 		dx = (b + a)/2;
 69 		dy = (max + min)/2;
 70 
 71 		//точки
 72 		//points = 100;
 73 	}
 74 
 75 	function calculation(){
 76 
 77 		cur_points++;
 78 
 79 		//положительная функция
 80 		if (min * max >= 0 && min >= 0 && n < points){
 81 			x[n] = Math.random() * (b - a) + a;
 82 			y[n] = Math.random() * (max - 0) + 0;
 83 
 84 			if (y[n] < f(x[n])){
 85 				ok++;
 86 			}
 87 
 88 
 89 			result = (ok / cur_points) * (b - a) * max;
 90 			n++;
 91 
 92 		}
 93 
 94 		//отрицательная функция
 95 		if (min * max >= 0 && max <= 0 && n < points){
 96 			x[n] = Math.random() * (b - a) + a;
 97 			y[n] = Math.random() * (min - 0) + 0;
 98 
 99 			if (y[n] > f(x[n])){
100 				ok++;
101 			}
102 
103 			result = -(ok/cur_points) * (b - a) * (-min);
104  			n++;
105 		}
106 
107 		//знакопеременные функции
108 		if (min * max < 0 && n < points){
109 
110 			x[n] = Math.random() * (b - a) + a;
111 			y[n] = Math.random() * (max - min) + min;
112 
113 
114 			if (y[n] > 0 && f(x[n]) > 0 && y[n] < f(x[n])){
115 				ok++;
116 			}
117 
118 			if (y[n] < 0 && f(x[n]) < 0 && y[n] > f(x[n])){
119 				ok--;
120 			}
121 
122 			result = (ok/cur_points) * (b - a) * (max - min);
123 			n++;
124 		}
125 	}
126 
127 	function draw(){
128 		//оси
129 		ctx.beginPath();
130 		ctx.moveTo(0 - dx * scalex, -h/2);
131 		ctx.lineTo(0 - dx * scalex, h/2);
132 		ctx.moveTo(w/2 , dy * scaley);
133 		ctx.lineTo(-w/2 , dy * scaley);
134 		ctx.stroke();
135 
136 		ctx.font = '10px Arial';
137 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
138 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
139 
140 
141 		//кривая
142 		ctx.beginPath();
143 		for (var i = a; i < b; i+=0.01){
144 			ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
145 			ctx.lineTo((i+0.01 - dx) * scalex, (-f(i+0.01) + dy) * scaley);
146 		}
147 
148 		ctx.stroke();
149 
150 
151 		//точки
152 		ctx.fillStyle = 'red';
153 		ctx.beginPath();
154 		ctx.arc((x[n-1] - dx) * scalex, (-y[n-1] + dy) * scaley, 1, 0, 2 * Math.PI);
155 		ctx.fill();
156 
157 	}
158 
159 	function control(){
160 		calculation();
161 		draw();
162 		result1.innerHTML = Math.round(result * 100)/100;
163 	}
164 
165 	knopka.onclick = function(){
166 
167 		if (flag){
168 			location.reload();
169 		}
170 
171 		flag = true;
172 		knopka.value = 'Очистить';
173 		cur_points = 0;
174 		points = parseFloat(document.getElementById("qual").value);
175 		dt = time/points;
176 		console.log(dt)
177 		a = parseFloat(document.getElementById("a1").value);
178 		b = parseFloat(document.getElementById("b1").value);
179 		search();
180 		var name = setInterval(control, dt);
181 	}
182 
183 
184 	if (n == points){
185 		clearInterval(name);
186 		console.log('a');
187 	}
188 }
189 
190 //Метод трапеций
191 window.addEventListener("load", program_code, false);
192 function program_code() {
193 
194   var ctx = canvas_example.getContext("2d");
195 	var w = canvas_example.width;
196 	var h = canvas_example.height;
197 
198   var flag = false;
199   var a;
200   var b;
201   var func;
202   var max = -100000;
203   var min = 100000;
204   var scale, scale1, scale2;
205   var x = [];
206   var y = [];
207   var result = 0;
208 
209 	ctx.translate(w/2, h/2);
210 
211   //функция
212   function f(x){
213     return (eval(func));
214   }
215 
216   function input(){
217 
218     a = parseFloat(document.getElementById("a1").value);
219 		b = parseFloat(document.getElementById("b1").value);
220     func = document.getElementById("fun").value;
221     number = parseFloat(document.getElementById('qual').value);
222 
223     //минимум и максимум
224     for (var i = a; i < b; i+=0.001){
225 
226 			//максимум
227 			if (f(i) > max){
228 				max = f(i);
229 			}
230 
231 			//минимум
232 			if (f(i) < min){
233 				min = f(i);
234 			}
235 		}
236 
237     //масштаб
238     scaley = 100/(Math.abs(max) + Math.abs(min));
239 
240     if (Math.abs(b) >= Math.abs(a)){
241       scalex = 250/b * 0.9;
242     }
243 
244     if (Math.abs(b) < Math.abs(a)){
245       scalex = 250/Math.abs(a) * 0.9;
246     }
247 
248     //сдвиг
249     dx = (b + a)/2;
250     dy = (max + min)/2;
251     dt = (b - a)/number;
252 
253     //разбиение
254     for (var i = a; i < b + 1/2 * dt; i += dt){
255       x.push(i);
256       y.push(f(i));
257     }
258   }
259 
260   function calculation(){
261     for (var i = 0; i < number; i++){
262 
263       if (f(x[i]) >= 0 && f(x[i+1]) >= 0){
264         result += (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
265       }
266 
267       if (f(x[i]) < 0 && f(x[i+1]) < 0){
268         result -= (x[i + 1] - x[i]) * (Math.abs(y[i]) + Math.abs(y[i + 1])) * 0.5;
269       }
270 
271       else{
272         result += 0;
273       }
274 
275     }
276   }
277 
278   function draw(){
279 
280     //оси
281 		ctx.beginPath();
282 		ctx.moveTo(0 - dx * scalex, -h/2);
283 		ctx.lineTo(0 - dx * scalex, h/2);
284 		ctx.moveTo(w/2 , 0 + dy * scaley);
285 		ctx.lineTo(-w/2 , 0 + dy * scaley);
286 		ctx.stroke();
287 
288     ctx.font = '10px Arial';
289 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
290 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
291 
292     //кривая
293     ctx.beginPath();
294     for (var i = a; i < b; i+=0.01){
295       ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
296       ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
297     }
298     ctx.stroke();
299 
300 
301     ctx.strokeStyle = 'red';
302 
303     //разбиение
304     ctx.beginPath();
305     for (var i = 0; i < number + 1; i++){
306       ctx.moveTo((x[i] - dx) * scalex, dy * scaley);
307       ctx.lineTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley)
308     }
309     ctx.stroke();
310 
311     ctx.beginPath();
312     for(var i = 0; i < number; i++){
313       ctx.moveTo((x[i] - dx) * scalex, (-y[i] + dy) * scaley);
314       ctx.lineTo((x[i+1] - dx) * scalex, (-y[i+1] + dy) * scaley);
315     }
316     ctx.stroke();
317 
318   }
319 
320 
321   knopka.onclick = function(){
322 
323     if (flag){
324       location.reload();
325     }
326 
327     flag = true;
328     knopka.value = 'Очистить';
329     input();
330     calculation();
331     result1.innerHTML = Math.round(result * 100)/100;
332     draw();
333   }
334 }
335 
336 
337 //Метод прямоугольников
338 window.addEventListener("load", program_code, false);
339 function program_code() {
340 
341   var ctx = canvas_example.getContext("2d");
342 	var w = canvas_example.width;
343 	var h = canvas_example.height;
344 
345   var flag = false;
346   var a;
347   var b;
348   var func;
349   var max = -100000;
350   var min = 100000;
351   var scale, scale1, scale2;
352   var x = [];
353   var y = [];
354   var result = 0;
355   var dt;
356   var dx = 0;
357   var dy = 0;
358 
359   ctx.translate(w/2, h/2);
360 
361   //функция
362   function f(x){
363     return (eval(func));
364   }
365 
366   function input(){
367 
368     a = parseFloat(document.getElementById("a1").value);
369 		b = parseFloat(document.getElementById("b1").value);
370     func = document.getElementById("fun").value;
371     var number = parseFloat(document.getElementById('qual').value);
372     dx = (b - a)/number;
373 
374     //минимум и максимум
375     for (var i = a; i < b; i+=0.001){
376 
377 			//максимум
378 			if (f(i) > max){
379 				max = f(i);
380 			}
381 
382 			//минимум
383 			if (f(i) < min){
384 				min = f(i);
385 			}
386 		}
387 
388     //масштаб
389     scaley = 100/(Math.abs(max) + Math.abs(min));
390 
391 		if (Math.abs(b) >= Math.abs(a)){
392 			scalex = 250/b * 0.9;
393 		}
394 
395 		if (Math.abs(b) < Math.abs(a)){
396 			scalex = 250/Math.abs(a) * 0.9;
397 		}
398 
399     //сдвиг
400 		dx = (b + a)/2;
401 		dy = (max + min)/2;
402     dt = (b - a)/number;
403 
404   }
405 
406   function calculation(){
407 
408     if (menu.value == 'first'){
409       console.log('a');
410       for (var i = a; i < b; i += dt){
411 
412         if (f(i) >= 0 & f(i + dt) >= 0){
413           result += Math.abs(f(i))*dt;
414         }
415 
416         if (f(i) < 0 & f(i + dt) < 0){
417           result -= Math.abs(f(i))*dt;
418         }
419 
420         else{
421           result += 0;
422         }
423 
424       }
425     }
426 
427     if (menu.value == 'second'){
428       for (var i = a + dt; i < b; i += dt){
429         if (f(i) >= 0 & f(i + dt) >= 0){
430           result += Math.abs(f(i))*dt;
431         }
432 
433         if (f(i) < 0 & f(i + dt) < 0){
434           result -= Math.abs(f(i))*dt;
435         }
436 
437         else{
438           result += 0;
439         }
440       }
441     }
442 
443     if (menu.value == 'third'){
444       for (var i = a + dt/2 ; i < b; i += dt){
445         if (f(i) >= 0 & f(i + dt) >= 0){
446           result += Math.abs(f(i))*dt;
447         }
448 
449         if (f(i) < 0 & f(i + dt) < 0){
450           result -= Math.abs(f(i))*dt;
451         }
452 
453         else{
454           result += 0;
455         }
456       }
457     }
458 
459   }
460 
461   function draw(){
462 
463     //оси
464 		ctx.beginPath();
465 		ctx.moveTo(0 - dx * scalex, -h/2);
466 		ctx.lineTo(0 - dx * scalex, h/2);
467 		ctx.moveTo(w/2 , 0 + dy * scaley);
468 		ctx.lineTo(-w/2 , 0 + dy * scaley);
469 		ctx.stroke();
470 
471     ctx.font = '10px Arial';
472 		ctx.strokeText('1', (1 - dx) * scalex, (-0.1 + dy) * scaley);
473 		ctx.strokeText('1', (0.1 -dx) * scalex, (-1 + dy) * scaley);
474 
475     //кривая
476     ctx.beginPath();
477     for (var i = a; i < b; i+=0.01){
478       ctx.moveTo((i - dx) * scalex, (-f(i) + dy) * scaley);
479       ctx.lineTo((i + 0.01 - dx) * scalex, (-f(i + 0.01) + dy) * scaley);
480     }
481     ctx.stroke();
482 
483     ctx.strokeStyle = 'red';
484 
485     if (menu.value == 'first'){
486       for (var i = a; i < b - dt/2; i += dt){
487         if(f(i) >= 0){
488           ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
489         }
490         else{
491           ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
492         }
493       }
494     }
495 
496     if (menu.value == 'second'){
497       for (var i = a + dt; i < b + dt/2; i += dt){
498         if(f(i) >= 0){
499           ctx.strokeRect((i - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
500         }
501         else{
502           ctx.strokeRect((i - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
503         }
504       }
505     }
506 
507     if (menu.value == 'third'){
508       for (var i = a + dt/2; i < b + dt/4; i += dt){
509         if(f(i) >= 0){
510           ctx.strokeRect((i - dt/2 - dx) * scalex, (-f(i) + dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
511         }
512         else{
513           ctx.strokeRect((i - dt/2 - dx) * scalex, (dy) * scaley, dt * scalex, Math.abs(f(i)) * scaley);
514         }
515       }
516     }
517 
518   }
519 
520   knopka.onclick = function(){
521     if (flag){
522       location.reload();
523     }
524 
525     flag = true;
526     knopka.value = 'Очистить';
527     input();
528     calculation();
529     draw();
530     result1.innerHTML = Math.round(result * 100)/100;
531   }
532 
533 }